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The dynamics of one-dimensional quantum droplets and the landing applicationsof deep learning are recent research hotspots. In this work, we propose a noveltime piecewise physics-informed neural networks (PINNs) to study complexdynamics on the one-dimensional quantum droplets by solving the correspondingamended Gross-Pitaevskii equation. The training effect of this network model inthe long time domain is far better than that of the conventional PINNs, andeach of its subnetworks is independent and highly adjustable. By using timepiecewise PINNs with scarce training points, we not only study intrinsicmodulation of single droplet and collision between two droplets, but alsoexcite the breathers on droplet background. Intriguingly, we obtain aninterference pattern from training result of collision between two droplets,which is a significant feature of the interplay of coherent matter waves. Thenumerical results showcase that different parameters may lead to completelydifferent dynamic behaviors under the same initial condition in a nonlinearnon-integrable system. Our results provide the significant guidance forintrinsic modulation of single droplet, droplet collision and breathersexcitation via deep learning technology.

Complex dynamics on the one-dimensional quantum droplets via time piecewise PINNs